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Chapter9.ppt

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Chapter 9

Place Value, Geometry,

Data Analysis and Measurement

Pertains to understanding that the same numeral represents different amounts depending upon which position it is in
One of the most difficult concepts for children to grasp
Must be understood before proceeding on to double digit and multidigit operations

Examples:

Ten 1s can be traded for one 10

One 10 can be traded for 10 ones

Ten 10s can be traded for one 100

One hundred 1s can be traded for one 100

Used to be referred to as borrowing and carrying
Happens when one or more items are added or taken away so that the amount moves to the next 10, and so on

Occurs after items are added or taken away (regrouping)
Example:

The group breaks down to three 10s and 5 units.
It is named 35.

8 units are added, so there are 13 units. Ten units are moved to the 10s place, leaving 3 in the 1s place (regrouping).

There are now four 10s and 3 units. The group is renamed 43.

Base-ten blocks
Cuisinaire rods
Montessori checkerboards
Place value boards
Trading games
Calculators and other technology tools

Points—small dots on paper
Curves—smooth, but not straight paths that connect two points
Lines—number lines in measuring or sides of geometric figures
Angles—space made by the meeting of two straight lines
Congruency—sameness of size and shape
Symmetry—correspondence of parts of a figure on opposite sides of a point or line

Geoboard problems
Study of geometric solids
Exploration of Symmetry
Using numberlines
Robotics and Lego Logo

Children can engage in more complex design technology projects combining Science, Technology, Engineering, and Mathematics.

Four most popular types:

picture graphs

bar graphs or histograms

line graphs

circle or pie graphs

The first two are the easiest for young children
Some primary children can begin to work with line graphs
Circle or pie graphs are too difficult for primary level children
Coordinates may be introduced

Used to organize data before it is graphed

Primary children are not ready for formal algebraic equations
Primary children can learn patterns using geometric shapes as variables

Example: Jerry has 5¢. He wants to buy a candy bar that costs 15¢.

5 + = 15

An important activity at the primary level
Children can begin to make rational estimates

Can the child follow directions and maintain involvement in the activities?
Does the child have the basic idea, but just needs practice and guidance?
Is the activity beyond the child’s ability?

An extremely important aspect of mathematics
A practical activity used in everyday life
An essential part of data gathering in science
A major vehicle for integrating mathematics with other content areas
A vehicle for reinforcing other mathematics skills
An area that lends itself naturally to problem-solving activities
Counting, whole number operations, and fractions are used to arrive at measurements and report results

Select an appropriate unit and tool for the attribute being measured
Measure objects that require a repeated use of the same tool
Use a variety of tools for measuring
Be able to make comparisons and estimates of standard unit measurements

Introduce

meaning of measurement

needed terminology

important units

most common measurement tools

English units

customary in the United States

Metric units

principal system in most countries

based on 10s

Use a sequenced approach

make comparisons that do not require numbers

use nonstandard arbitrary units

find the number of units by counting

report the number of units

compare the thing measured to the units

introduce standard units appropriate for the same type of measurement

find the number of units using standardized tools

report the number of units

The ability to measure rests on understanding the concept of unit
Perceiving that units can be other than 1 may be difficult for children

a unit may be

two degrees

one-half foot

three centimeters

The use of nonstandard units first helps develop the concept of unit

Through the use of arbitrary units children learn

that measurement can be made with an arbitrary unit

that smaller units require more units than larger units

that they must be accurate

that there are shortcuts to measurement

Begin with simple tools that are marked only with the unit being measured
Be sure the children understand how the units are marked
Children must be able to apply their addition and fraction skills

Present a problem where every individual unit is not marked

Example: Thermometers are marked every two degrees

Have the children make their own instruments

The analog clock is one of the most difficult instruments for children to understand (digital clocks are much easier).

due to the circular movement of the hands, the face is difficult to read for children

there is no set age for being able to tell time

skills for reading time are learned over many years and through practice with clock faces with moveable hands

Another difficult instrument for children to learn

the size of the units (coins) does not correspond with the value of the unit

Examples:

pennies are larger than dimes

bills give no size cues

relating coins to bills is difficult for children